I should have mentioned that my husband doesn't want to paint the door.

Behr Chick Taupe color would work

or lighter version

Warm gray

I think color you have next to the door works great

celerygirl, can you photoshop the entryway with navy for the wall color?

The other issue is that we're having a built-in bench and shelves and coat hooks put where all the painting equipment is, and I want navy beadboard for the back of that wall but whatever off-white wall color we use for the shelves. So if I choose a more colorful/darker off-white for the wall, I think the color will look funny on the shelves.

The taupe color loooks nice, but I think I would have to scrap the navy beadboard if I did that, and I'd still have to choose a white for the shelves.

I would change the slate to just more travertine since IMO those 2 floors do not work together at all then choosing paint will be easier for sure and I would stain the door one of the other wood colors you have or paint it. I think you are trying to mix too many colors and it will make you crazy. I have no idea why the navy beadboard at all in the mix.

My husband doesn't want to paint the door, unfortunately. I like the look of beadboard or shiplap behind entryway/mudroom built-ins, and want some color somewhere. It's frustrating having only whites for the walls and having to choose a lot of my decor based on existing finishes that I can't change any time soon (travertine, blue carpet in both the master bedroom and living room).

Is it that he doesn’t want to do the physical labor of painting or that he likes the stain?

Practically everyone has challenges with existing finishes, very few can afford to rip everything out and start from scratch. Sometimes it's just one element (in my case, an existing kitchen granite than I don't really like but am unwilling to tear out), other times it's several. In your home, you have three different floorings that don't really go together, all in one small area.

The best way to treat disparate elements is to tie them together with a neutral, in this case paint. I'd just continue the same paint you have in your living room into your entry/hallway. It may seem a little boring, but better boring than to add yet another color to an already odd mix. It may not go perfectly with the travertine, but it's probably more than "good enough" and once art and accessories are in you'll probably not think twice about it.

Your burgundy LR couches echo the darker tones in the slate entry(note: not perfectly match, but echo the darker color), so pull some of the blue carpet and slate colors into your hallway with art/accessories. That will help tie these three areas together. The one thing I do not see in this entry is bead board and navy paint. The bead board has absolutely nothing in common with the traditional elements seen here, and you don't need to add navy paint to this mix. I would advise maybe trying to echo the wood stain color of your handrail and the wood column (?) in your second pic.

Maybe he doesn't want to paint the door because he's thinking of the outside door color, but you can just paint the inside of the door. It doesn't match your other woods, and is very limiting. Also, navy is never going to work with a reddish door and dark gray floor. Or, as Patricia suggested, continue the travertine into the entry, which would allow you to keep the door and use the navy with cream walls. Or, use a darker wall color on the walls and paint the builtin the cream color from the other walls. One of your items needs to change in order to work together.

I'm not really an artist, and I don't know the dimensions of the area you want to do built-ins, but this is a quick sketch of something that I would do, rather than bead board and navy paint:

I'd do two side cupboards that mimic that wooden panel area you already have, with the center area being a hinged seat that can provide additional storage. Make it in oak and stain it the same color as the existing wood in that area. Put a cushion in an outdoor/performance fabric on it. The back area would be drywall, painted your wall color, with large hooks for coats.

I'd use a fabric such as this for your living room drapes. It ties in the blue and burgundy colors, and works with your wall color and the travertine. (Source: Ballard Designs)

A pretty performance fabric on the entry seat could pull in the blue you want. (Source: Ballard Designs)

I'd paint the inside of your front door a color such as SW Urbane Bronze, and also a dresser/entry table opposite it. That would add a punch of color and also work with all the different floorings. Maybe a lamp on the entry table in a blue-and-white porcelain.

He doesn't want to paint the door at all. I could suggest painting it to match the walls and see what he says.

The built-in is supposed to match the wall color and have a stained bench. Something like the drawing the pp showed but open shelves instead of cabinets and open under the bench for shoes and boot trays. I was wanting walnut for the bench and no cushion as the living room trim is all walnut and the floor trim in the entryway is sort of a faded walnut (wanting to restain that to match the living room walnut).

Is taupe any better of a paint color for the entryway? Taupe walls, white built-in, ivory for the hallway? The slate floor will be mostly covered by an indoor/outdoor rug.

Maybe it's just not possible for this house to look nice. I'm fighting all the things that aren't changing about the house, and it seems like everything I want to do doesn't "go" with the house. Also fighting my husband's strong opinions and his traditional/rustic man-cave taste.

So don't paint the door. It seems silly to me, but not worth fighting over.

Yes, it's possible for your house to look nice. The problem is you have a house with a lot of really different/mismatched design ideas, and the goal is to create a more cohesive feel. Bead board and navy paint = wrong.

It's important to identify what things you can/will replace, and what will stay. I can see you replacing the living room carpet eventually, but not the travertine flooring. So it's important to make design decisions that will work with that. Same with the wood trim.

That's why I mentioned that the entry cubby should echo the wood trim in the living room. It will make that trim look intentional, rather than random. And while I know you want open shelves, this is in your entry not a garage entry/mudroom. I think cupboards will help hide items that are best not on display.

The living room trim doesn't look random because that trim is throughout the main level except for the master bedroom. The oak is what seems random to me because it's only there in the hallway, though in multiple areas (banister, wood column that's hiding an old chimney, and built-in shelves next to the column. The door stain is kind of random also. The whole has random elements because the previous owners really went to town with "upgrades", but they choose a lot of different finishes, so the main living area has four different wood colors between the door stain, walnut trim, the oak, and hickory cabinets in the kitchen. Maybe I can stain the oak to match the walnut trim at some point.

I don't think the entryway shelves will look cluttered because there will be baskets on all of them to hold shoes etc. DH didn't want cupboards, and the kids would probably break doors on them anyway.

It's hard to figure out what will eventually go and what won't. There's a whole lot that I'd like to replace/redo, but DH doesn't really want to do any of it, so...

I'm leaning toward keeping the beadboard but painting it the wall color. I had a designer come today and she said beadboard would look ok if it was painted the wall color. Also, the dining room, which is visible from the entryway, has a narrow strip type of wainscoting that is reminiscent of beadboard, though stained walnut color, so I don't think it will look too out of place.